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Chapter 9 - PowerPoint PPT Presentation

Chapter 9. Momentum and Its Conservation. What’s the relationship between force and velocity?. What happens when the baseball is struck by the bat? _______________tells us that the forces on the bat and ball are equal.

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Chapter 9

Momentum and Its Conservation

• What happens when the baseball is struck by the bat?

• _______________tells us that the forces on the bat and ball are equal.

• _______________tells us that both bat and ball will experience an acceleration proportional to their masses.

• But what is the relationship between the velocities of the ball and the bat and the forces they experience?

• The ________________ of an object of mass m moving with a velocity is defined as the __________ of the ______ and the __________.

• SI Units are kg m/s (Dimensions = ML/T)

• Vector quantity, the direction of the momentum is the same as the velocity’s.

• Momentum components:

• px = m vx and py = m vy

• Applies to two-dimensional motion.

• Again the direction of momentum and velocity are the same.

• Momentum is related to ________________.

• We can derive an equation that relates KE and momentum.

• More on kinetic energy in chapter 10.

• How does an object change its acceleration?

• How would an object change its momentum?

• In order to change the momentum of an object, a _______________ must be applied.

• The _________of change of momentum of an object is equal to the __________acting on it.

• Just like with acceleration, when the __________is zero, no change occurs to momentum.

• Gives an alternative statement of Newton’s second law.

• When a single, constant force acts on the object, there is an ____________ delivered to the object.

• is defined as the impulse.

• ____________________, the direction is the same as the direction of the __________.

• The impulse is also described using the letter J.

• Impulse is useful for describing ______________ that do not last a long time. (More on this later.)

• The theorem states that the ___________ acting on the object is equal to the ___________________ of the object.

• This theorem holds for _________ and ____________ forces.

• If the force is not constant, use the average forceapplied.

Rico strikes a 0.058 kg golf ball with a force of 272 N and gives it a velocity of 62.0 m/s. How long was Rico’s club in contact with the ball?

• The ______________can be thought of as the constant force that would give the same impulse to the object in the time interval as the actual time-varying force gives in the interval.

Average Force and collisions

• Impulse is most useful in describing _________ of _______________.

• The impulse-momentum theorem allows us to study the effects that the ________________of a collision has on the _________ felt by the ____________.

• For example, why is it important for boxers to wear boxing gloves?

• _____________ the contact time increases the ___________ but reduces the _________ during the collision.

• Increasing force increases the impulse as well.

• The most important factor is the ___________or the time it takes the person to come to a rest.

• Increasing the collision time is the key factor.

• This will reduce the chance of dying in a car crash.

• Crumple zones

• Air

• bags

• Seat

• belts

• For a 75 kg person traveling at 27 m/s and coming to stop in 0.010 s.

• F = -2.0 x 105 N

• a = 280 g

• Almost certainly fatal:

• F = 90 kN fractures bone.

• a = 150 g for 4 ms causes spinal cord damage (causes the nerves to enter the base of the brain)

• ______________ is conserved in any _________.

• ______________is not always conserved.

• Some KE is converted to other forms of energy (i.e. internal energy, sound energy, etc.) or is used to do the work needed to deform an object.

• Two broad categories of collisions:

• Elastic collisions

• Inelastic collisions: Perfectly inelastic and inelastic

• Elastic and perfectly inelastic collisions represent ideal cases of collisions.

• Most real world cases fit somewhere between these two extremes.

• Momentum in an isolated system in which a collision occurs is conserved.

• A collision may be the result of _______________ between two objects.

• “Contact” may also arise from the ______________ interactions of the electrons in the surface atoms of the bodies.

• An isolated system will have no external forces acting on the objects.

Conservation of Momentum

• The principle of conservation of momentum states when no external forces act on a system consisting of two objects that collide with each other, the total momentum of the system remains constant in time.

• Specifically, the total momentum before the collision will equal the total momentum after the collision.

F

• The force with which object 1 acts on object 2 is equal and opposite to the force with which object 2 acts on object 1.

• Impulses are also equal and opposite.

Conservation of Momentum formula

• Mathematically:

• Momentum is conserved for the system of objects.

• The system includes _____________________ interacting with each other.

• Assumes only internal forces are acting during the collision.

• Can be generalized to any number of objects.

A 1875 kg car going 23 m/s rear-ends a 1025 kg compact car going 17 m/s on ice in the same direction. The two cars stick together. How fast do the two cars move together immediately after the collision?

• Xe atoms are expelled from the ion engine.

• vatoms = 30km/h; Fatoms = 0.092 N

• Advantage: runs for a very long time

• For a general collision of two objects in three-dimensional space, the conservation of momentum principle implies that the total momentum of the system in each direction is conserved.

• Use subscripts for identifying the object, initial and final velocities, and components.

• We will examine collisions in two-dimensions.

• The “after” velocities have x and y components.

• Momentum is conserved in the x direction and in the y direction.

• Apply conservation of momentum separately to each direction.

A 1,500 kg car traveling east with a speed of 25.0 m/s collides at an intersection with a 2,500 kg van traveling north at a speed of 20.0 m/s as shown in the figure. Find the direction and magnitude of the velocity of the wreckage after the collision, assuming that the vehicles undergo a perfectly inelastic collision and assuming that friction between the vehicles and the road can be neglected.

END

Chapter 9

Momentum and Its Conservation